Hawking temperature in the eternal BTZ black hole: an example of holography in AdS spacetime

We review the relation between AdS spacetime in 1 $+$ 2 dimensions and the BTZ black hole (BTZbh). Later we show that a ground state in AdS spacetime becomes a thermal state in the BTZbh. We show that this is true in the bulk and in the boundary of AdS spacetime. The existence of this thermal state is tantamount to say that the Unruh effect exists in AdS spacetime and becomes the Hawking effect for an eternal BTZbh. In order to make this we use the correspondence introduced in algebraic holography between algebras of quasi-local observables associated to wedges and double cones regions in the bulk of AdS spacetime and its conformal boundary respectively. Also we give the real scalar quantum field as a concrete heuristic realization of this formalism.     

A uniqueness theorem for the anti-de Sitter soliton

The stability of physical systems depends on the existence of a state of least energy. In gravity, this is guaranteed by the positive energy theorem. For topological reasons, this fails for nonsupersymmetric Kaluza-Klein compactifications, which can decay to arbitrarily negative energy. For related reasons, this also fails for the anti-de Sitter (AdS) soliton, a globally static, asymptotically toroidal Lambda<0 spacetime with negative mass. Nonetheless, arguing from the AdS conformal field theory (AdS/CFT) correspondence, Horowitz and Myers proposed a new positive energy conjecture, which asserts that the AdS soliton is the unique state of least energy in its asymptotic class. We give a new structure theorem for static Lambda<0 spacetimes and use it to prove uniqueness of the AdS soliton. Our results offer significant support for the new positive energy conjecture and add to the body of rigorous results inspired by the AdS/CFT correspondence.     

New massive gravity and AdS(4) counterterms

We show that the recently proposed Dirac-Born-Infeld extension of new massive gravity emerges naturally as a counterterm in four-dimensional anti-de Sitter space (AdS(4)). The resulting on-shell Euclidean action is independent of the cutoff at zero temperature. We also find that the same choice of counterterm gives the usual area law for the AdS(4) Schwarzschild black hole entropy in a cutoff-independent manner. The parameter values of the resulting counterterm action correspond to a c=0 theory in the context of the duality between AdS(3) gravity and two-dimensional conformal field theory. We rewrite this theory in terms of the gauge field that is used to recast 3D gravity as a Chern-Simons theory.     

On unitary subsectors of polycritical gravities

We study higher-derivative gravity theories in arbitrary space–time dimension $d$ with a cosmological constant at their maximally critical points where the masses of all linearized perturbations vanish. These theories have been conjectured to be dual to logarithmic conformal field theories in the $(d-1)$ -dimensional boundary of an AdS solution. We determine the structure of the linearized perturbations and their boundary fall-off behaviour. The linearized modes exhibit the expected Jordan block structure and their inner products are shown to be those of a non-unitary theory. We demonstrate the existence of consistent unitary truncations of the polycritical gravity theory at the linearized level for odd rank.     

The relations between the multipole moments in axistationary electrovacuum spacetimes and the N-soliton solution

General Relativity and Gravitation - We investigate the behavior of the deflection of light rays by charged and rotating AdS black holes using the Gauss–Bonnet formalism. Taking weak field...     

Constraints on braneworld gravity models from a kinematic limit on the age of the black hole XTE J1118+480

In braneworld gravity models with a finite anti-de Sitter space (AdS) curvature in the extra dimension, the AdS/conformal field theory correspondence leads to a prediction for the lifetime of astrophysical black holes that is significantly smaller than the Hubble time, for asymptotic curvatures that are consistent with current experiments. Using the recent measurements of the position, three-dimensional spatial velocity, and mass of the black hole XTE J1118+480, I calculate a lower limit on its kinematic age of > or =11 Myr (95% confidence). This translates into an upper limit for the asymptotic AdS curvature in the extra dimensions of <0.08 mm, which significantly improves the limit obtained by table top experiments of sub mm gravity.     

一类新的Stückelberg全息超导模型

本文研究了含Stückelberg机理的黑洞全息超导模型. 通过选取标量场新的高阶修正形式, 建立了新的Stückelberg黑洞全息超导模型. 通过研究模型参数对标量场凝聚的影响, 发现了当模型参数大于临界值时, 高阶修正可以引起一阶相变. 同时本文还考查了反作用对临界值的影响.     

Massive Vector Particles Tunneling from the Neutral Rotating Anti-de Sitter Black Holes in Conformal Gravity

We investigate the massive vector particles' Hawking radiation from the neutral rotating Anti-de Sitter(AdS) black holes in conformal gravity by using the tunneling method.It is well known that the dynamics of massive vector particles are governed by the Proca field equation.Applying WKB approximation to the Proca equation,the tunneling probabilities and radiation spectrums of the emitted particles are derived.Hawking temperature of the neutral rotating AdS black holes in conformal gravity is recovered,which is consistent with the previous result in the literature.     

Entanglement entropy and gravity/condensed matter correspondence

The entanglement entropy has been very important in various subjects such as the quantum information theory, condensed matter physics and quantum gravity. Especially, for more than twenty years, this quantity has been studied by many people in order to obtain a quantum mechanical interpretation of the gravitational entropy such as the black hole entropy. We will introduce recent progresses toward this long-standing problem in quantum gravity by applying the idea of holography, especially the AdS/CFT correspondence found in string theory. We will explain the holographic formula which computes the entanglement entropy of quantum field theories in terms of the area of minimal surfaces in general relativity. We will also review the recent application of AdS/CFT correspondence to condensed matter physics from the viewpoint of entanglement entropy.     

S-duality in 3D gravity with torsion

The deformation of the connection in three spacetime dimensions by the kinematically equivalent coframe is shown to induce a duality between the (Lorentz-) rotational and translational field momenta, for which the coupling to the deformation parameter is inverted. This new kind of strong/weak duality, pertinent to 3D, is instrumental for studying exact solutions of the 3D Poincaré gauge field equations and the particle content of propagating modes on a background of constant curvature. For a topological Chern-Simons model of gravity, the propagating modes ‘living’ on an Anti-de Sitter (AdS) background correspond to real massive particles. Yang-Mills type generalizations and new cubic Lagrangians are found and completely classified in 3D. AdS or black hole type solutions with constant axial torsion emerge, also for these higher-order Lagrangians with new ‘exotic’ torsion-curvature couplings. Their pattern complies with our S-duality, with new repercussions for the field redefinition of the metric in 3D quantum gravity and the cosmological constant problem.     

Anisotropic conformal infinity

We generalize Penrose’s notion of conformal infinity of spacetime, to situations with anisotropic scaling. This is relevant not only for Lifshitz-type anisotropic gravity models, but also in standard general relativity and string theory, for spacetimes exhibiting a natural asymptotic anisotropy. Examples include the Lifshitz and Schrödinger spaces (proposed as AdS/CFT duals of nonrelativistic field theories), warped AdS ₃, and the near-horizon extreme Kerr geometry. The anisotropic conformal boundary appears crucial for resolving puzzles of holographic renormalization in such spacetimes.     

Classical geometry to quantum behavior correspondence in a virtual extra dimension

In the Lorentz invariant formalism of compact space–time dimensions the assumption of periodic boundary conditions represents a consistent semi-classical quantization condition for relativistic fields. In Dolce (2011) [18] we have shown, for instance, that the ordinary Feynman path integral is obtained from the interference between the classical paths with different winding numbers associated with the cyclic dynamics of the field solutions. By means of the boundary conditions, the kinematical information of interactions can be encoded on the relativistic geometrodynamics of the boundary, see Dolce (2012) [8]. Furthermore, such a purely four-dimensional theory is manifestly dual to an extra-dimensional field theory. The resulting correspondence between extra-dimensional geometrodynamics and ordinary quantum behavior can be interpreted in terms of AdS/CFT correspondence. By applying this approach to a simple Quark–Gluon–Plasma freeze-out model we obtain fundamental analogies with basic aspects of AdS/QCD phenomenology.     

Axiomatic Conformal Theory in Dimensions &gt;2 and AdS/CT Correspondence

We formulate axioms of conformal theory (CT) in dimensions >2 modifying Segal’s axioms for two-dimensional CFT. (In the definition of higher-dimensional CFT, one includes also a condition of existence of energy-momentum tensor.) We use these axioms to derive the AdS/CT correspondence for local theories on AdS. We introduce a notion of weakly local quantum field theory and construct a bijective correspondence between conformal theories on the sphere S^d and weakly local quantum field theories on \({H^{d+1}}\) that are invariant with respect to isometries. (Here \({H^{d+1}}\) denotes hyperbolic space = Euclidean AdS space.) We give an expression of AdS correlation functions in terms of CT correlation functions. The conformal theory has conserved energy-momentum tensor iff the AdS theory has graviton in its spectrum.     

Gravitation,thermodynamics, and the bound on viscosity

The anti-de Sitter/conformal field theory (AdS/CFT) correspondence implies that small perturbations of a black hole correspond to small deviations from thermodynamic equilibrium in a dual field theory. For gauge theories with an Einstein gravity dual, the AdS/CFT correspondence predicts a universal value for the ratio of the shear viscosity to the entropy density, η/s = 1/4π. It was conjectured recently that all fluids conform to the lower bound η/s ≥ 1/4π. This conjectured bound has been the focus of much recent attention. However, despite the flurry of research in this field we still lack a proof for the general validity of the bound. In this essay we show that this mysterious bound is actually a direct outcome of the interplay between gravity, quantum theory, and thermodynamics.